In a medium bowl, beat together butter and sugars until creamy. Beat in egg white and vanilla until smooth. Add dry ingredients and stir by hand just until combined.

Between two sheets of parchment paper, roll the dough into a 12" square. Place in the refrigerator until firm, about 30 minutes. Remove from the refrigerator and remove the top piece of parchment.

For the assembly and filling

Drizzle golden syrup evenly over the dough - sprinkle the top with the brown sugar, cinnamon and nuts, going almost to edges. Gently roll up the dough into a log, peeling back the bottom piece of parchment as you go. Wrap the dough with plastic wrap and place in the freezer until firm, about 3 hours.

Preheat oven to 350

Remove dough from the freezer and unwrap. With a sharp knife, slice the log into 1/4" thick rounds - place onto parchment lined baking sheets. Bake until the cookies are a pale golden, about 12 to 15 minutes. Remove from the oven and let cool for a couple minutes on the baking sheet before transferring them to a wire rack to cool completely.

For the drizzle

In a small bowl, combine confectioners' sugar, milk and vanilla until smooth. Use a spoon or fork to drizzle mixture over the cookies.